Simplify the following expression: $\dfrac{40n^2}{36n^3}$ You can assume $n \neq 0$.
$ \dfrac{40n^2}{36n^3} = \dfrac{40}{36} \cdot \dfrac{n^2}{n^3} $ To simplify $\frac{40}{36}$ , find the greatest common factor (GCD) of $40$ and $36$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(40, 36) = 2 \cdot 2 = 4 $ $ \dfrac{40}{36} \cdot \dfrac{n^2}{n^3} = \dfrac{4 \cdot 10}{4 \cdot 9} \cdot \dfrac{n^2}{n^3} $ $\phantom{ \dfrac{40}{36} \cdot \dfrac{2}{3}} = \dfrac{10}{9} \cdot \dfrac{n^2}{n^3} $ $ \dfrac{n^2}{n^3} = \dfrac{n \cdot n}{n \cdot n \cdot n} = \dfrac{1}{n} $ $ \dfrac{10}{9} \cdot \dfrac{1}{n} = \dfrac{10}{9n} $